Optimal Smoothing for Guaranteed Service.

We consider the transmission of variable bit rate
(VBR) video over a network offering a guaranteed service such as ATM
VBR or the guaranteed service of the IETF. The guaranteed service requires
that the flow accepted by the network has to be conforming with a traffic
envelope s; in return, it receives a service guarantee expressed by
a network service curve ß. Functions s and ß are derived
from the parameters used for setting up the reservation, for example,
from the T-SPEC and R-SPEC fields used with the resource reservation
protocol (RSVP). In order to satisfy the traffic envelope constraint,
the output of the encoder is fed to a smoother, possibly with some
look-ahead. The resulting stream is transported by the network; at
the destination, the decoder waits for an initial playback delay and
reads the stream from the receive buffer. We consider the problem of
whether there exists one optimal strategy at the smoother which minimizes
the playback delay and the receive buffer size, given the traffic envelope
a and the service curve ß. We show that there does exist such
an optimal smoothing, and give an explicit representation for it. We
also obtain a simple expression for the smallest playback delay and
playback buffer size which can be achieved over all possible smoothing
and playback strategies. We show that the computation of optimal smoothing
and minimum playback delay do not depend on the past. We show that
separate delay equalization is optimal in the constant bit rate (CBR)
case, but not otherwise. We also apply the theory to the analysis of
which T-SPEC should be requested by a source-destination pair, given
some playback delay and buffer constraint, and given the path characteristics
advertised in RSVP PATH messages.